Art of reducing attenuation of electrical waves.



No. 652,23l. Patented June 59, 1900. .M. In PUPIN.

ART OF REDUCING ATTENUATION OF ELECTRICAL WAVEQS. (Applicltion filed lhy 28, 1900.)

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ART OF REDUCING ATTENUATION OF ELECTRICAL WAVES.

(Application filed MAY 98. 1900.)

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(No Model.)

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UNITED STATES PATENT OFFICE.

MIGlIAELlDVORSKY PUPIN, OF YONKERS, NEW YORK.

ART OF REDUCING ATTENUATION OF ELECTRICAL WAVES.

SPECIFICATION forming part of Letters Patent No. 652,231, d t d J 19, 1900.

Original application filed December 14,1899, Serial No. 740,238. Divided and this application filed May 28,1900. Serial No. 18,305. (No model.)

To all, 1071,0112, it may concern;

Be it known that 1, MICHAEL IDVORSKY PUPIN, a citizen of the United States of America, and a resident of Yonkers, county of lVestchester, and State of New York, have invented certain new and useful Improvements inlhe Art of Reducing Attenuation of Electrical \Vaves, of which the following is a specification.

My invention consists in an improvement in the construction and installation of conductorsfor the transmission of electrical energy by means of electrical waves, whereby by decreasing the current necessary to transmit the amount of energy required the attenuation of such waves is reduced, and therefore the efficiency of transmission is increased.

Electrical condnctors-say a given length of copper wire-possess ohmic resistance,selfinductance, and electrostatic capacity. A variable electrical current in such a conductor is accompanied by three distinct kinds of' reactionsviz., the resistance reaction, selfinductance reaction, and the displacement of electrostatic reaction. In overcoming these relations the impressed electromotive force does three kinds of work, which appear, respectively, as, first, heat generated in the conductor and as energy which is stored in the medium surrounding the conductor in the form of, second, magnetic and, third, electrostatic energy. The laws governing these three reactions. govern the flow of variable currents in wire conductors. A mathematical discussion of the laws of flow of variable currents in long wire conductors was first given by Prof. William Thomson, now LordKelvin, in 1855. His theory was considerably extended by the late Prof. G. Kirchhoff in 1857. Since that time the subject has been very extensively studied by many in vestigators, particularly in connection with the modern developments in telegraphy, telephony, and long-(listance transmission of power by alternating currents. I-have also been engaged for several years in experimental and mathematical researches of this subject, some of the results of which were given in a paper read before the American Institute of Electrical Engineers on March 22,

1899. This paper, which is entitled Propa-- thin plates.

gation ofLongElectrical \Vaves, is published in Vol. XV of the transactions of that society, and frequent references will be made to it in the course of this application.

In the accompanying drawings, which form a part of this specification, Figure 1 is a diagram illustrating a tuning-fork and a string to bevibrated thereby. Fig. 2 is a diagram illustrating the waves set up in this string when it is executing forced vibrations in air under the action of the tuning-fork. Fig. 3 is a diagram illustrating the same apparatus with the string executing forced vibrations in a medium which offers appreciable resistance to the vibrations of the string. Fig. 4 is a diagramillustrating an electrical generator of alternating currents and a conductor leading therefrom, the system being grounded at one end only. Fig. 5 is a diagram of an electrical wave propagated along the conductor of Fig. awhen the generatorimpresses a simple harmonic electromotive force upon the conductor. Fig. 6 is a diagram of a vibrating system similar to that of Fig. l, but with a string which is loaded by weights distributed uniformly along its length. Fig. 7

is a diagram illustrating the waves set up in this string when executing forced vibrations under the action of the tuning-fork in a medium which olfers appreciable resistance to the vibration of the string. Fig. 8 is a diagram illustrating what is here called a reactance-conductor of the first type. Fig. 9 is a diagram of a modified reaetance-conductor of the first type. Fig. 10 is ac'iiagram of a slow-speed conductor of the second type, called also in this specification a reactanceconductor. Figs. 11 and 12 are details of apparatus. Fig. 11 is a sectional view of a transformer having an iron core made up of Fig. 12 is the end view of the same transformer.

The main results of the theory of the propagation of electrical waves in long wire con ductors' should be stated here briefly for the purpose of placing the claims of this application in iheirtruelight. A mechanical analogy will add much to the clearness of this statement.

In diagram of Fig. 1, A B O is a tuning-fork which is rigidly fixed at its neck 0. To the free extremity of prong B is attached a heavy flexible string B D. This string is supposed to be under a certain tension, and one of its terminals is fixed at D. Its position of equilibrium is represented by the full line B D. Suppose now that the tuning-fork is made to vibrate steadily by an electromagnet or otherwise. The string will vibrate with it, the vibrations of the string being forced vibrationsthat is, vibrations which follow the period of the tuning-fork. Two 4 principal forms of vibration will be described here briefly. The form of stationary waves is represented in diagram of Fig. 2. This form is obtained when the intern al and external frictional resistances are negligibly small. The

' waves travel with undiminished amplitude.

Hence the direct wave coming from the tuning-fork and the reflected wave coming from the fixed point D will have the same amplitude, and therefore by their interference stationary waves will be formed with fixed 'nodes at a c e g D and ventral segments at b d f h. When, however, internal and external. frictional resistances are not negligibly small, then a progressive attenuated system of waves is formed, which is illustrated in diagram of Fig. 3. The amplitude of the wave is continually diminished in its progress from B to D on account of the frictional resistance. After its reflection MD the returning wave, having a smaller amplitude than the oncoming wave, cannot form by interference with it a system of stationary waves, The string therefore does not present to an observer a definite wave form, as in the case of stationary waves. Its appearance is continually changing. If, however, we observe. the string by means of a rotating mirror or by properly-timed electrical sparks we shall see the string as represented by curve a, b c d e f in Fig. 3. It is a wave .curve with continually-diminishing amplitude due .to attenuation. frictional-resistance reactions are proportional to the velocity, the attenuation ratio (the ratio of amplitudes of two successive half-waves) will bea constant quantity. The velocity of propagation which fixes the wave length fora given frequency and the attenuation ratio are the most characteristic constants of the curve. Both of these depend on the density of the string, its tension, frictional resistance, and frequency.v For instance, the greater the tension, other things being equal, the greater will be the velocity of propagation, and hence the longer the wave length for a given frequency. That which is of particular importance is the attenuation ratio and its relation to the density of the string.

By substituting strings of greater and greater I Assuming that the mits wave energy more efliciently than a light orgy or energy of motion of the strings mass and partly as potential energy or energy of deformation of the string. The process of propagation of a wave consists in the successive transformation of the kinetic part of the total energy into potential energy, and vice versa. During this transformation a part of the energy is lost as heat on account of the frictional reactions. These reactions are supposed to be proportionalto the velocity, so that the rate of loss due to these reactions will be proportional to the square of the velocity. Consider now the kinetic energy of an element of the string. It is proportional to the product of mass into the square ofits velocity. Making the mass n times as large we shall be able to store up in the element the same amount of kinetic energy with only l-nth of the velocity; but since the rate of dissipation into heat due to frictional resistances is proportional to the square of velocity, it follows that in the second case the element of the string transmits the same amount of energy with only l-nth part of the loss. In other words, the heat loss is inversely proportional to the density of the string. The physical-fact that dense strings transmit energy more efficiently than light ones is therefore reduced to the fundamental principle that dense strings require a smaller velocity in order to store up a given amount of kinetic energy, and smaller velocity means a smaller dissipation into heat and therefore a smaller attenuation of the wave. The denser the string the more nearly will its vibration approach the form of stationary waves.

The vibration of the string just considered isa perfect analogy to the propagation of electrical waves along wire conductor B D, Fig. 4, one end, B, of which is connected to generator 0 of simple harmonic electromotive 'force, the other pole of the generator being grounded at O. The existence of this analogy is due to the physical fact that the three reactions which accompany the vibration of a stringviz.,the acceleration reac- IIO tion, the tensional reaction, and the frictional reactionfollow the same laws as the threereactions which accompany the flow of a variable current in a long wire conductorviz., the ohmic-resistance reaction, inductancereaction, and the capacity reactionthat is to say, the ohmic resistance, the inductance, and the reciprocal of the capacity of the conductor, all per unit length, correspond, re-

spectively, to the coefficient of friction, the

density, and the tension of the string.

In Fig. 5 the line B D represents the wire conductor B D of-Fig. 4. The ordinates of the curve a" b" c d e f represent the instantaneous values of the current at the various points of the conductor. This current curve is of the same form as the curve of the string illustrated in Fig. 3. The magnetic energy of the current corresponds to the kinetic energy of the vibrating string, and just as a dense string transmits mechanical energy more efficiently than does alight string so a wire of large inductance per unit length will, under otherwise the same conditions, transmit energyin the form of electrical waves few numerical examples about to be discussed will illustrate this accurately and fully. Before discussing the examples I shall give two definitions. On page 122 of the paper on Propagation of .Long Electrical Waves mathematical expressions are given for the most important constants, to which the names of wave-length constant and attenuation constant are assigned in this application. The mathematical expressions for these constants, which are represented by symbols or and [5, respectively, are as follows:

$1) CA N p L l- 11 L},

L inductance of the wire per mile.

0 capacity of the wire per mile.

R ohmic resistance of the wire per mile.

T period of the impressed electromotive force.

The physical significance of these two constants can be stated in a simple manner. Let

A wave length. Then Hence the name wavelength constant, which is applied to it in this specification. Again, let a wave of amplitude U start from point B, Fig. 4. By the time it reaches a point at a distance 8 from 13" its amplitude will be U 6- where e is the base of Naperian logarithms. The constant [5 measures the attenuationhence the name attenuation constant which is assigned to it in this application. The expression 6 is called in this specification the attenuation factor, because it is the factor by which the initial amplitude has to be multiplied to get the amplitude at a point at a distance 8 from the source. I shall consider now two distinct numerical examples for the purpose of showing how these constants influence the transmission of electrical energy over long wire conductors.

Underground cables for telephonic communication in New York city are now constructed which have the following values per mile:

L 0, (very nearly.)

C I 5 X 10" far-ads.

R 20 ohms.

The formula for a' and [3 reduces this case to a M te 1i:

[i I c a;

Let I p z 2 7r X 3,000 2 1,900, (roughly) I select the frequency of three thousand p. p. s., because this is according to all authorities far beyond the highest frequency which occurs in the telephonic transmission of speech. I shall show that even for this high frequency the attenuation can be much reduced by adding inductance to the cable. \Ve get for this frequency The wave length 7t 5 (34 miles in round numbers.

U w U (2' This means that practically no current whatever reaches Boston. The ohmic resistance wipes out completely the wave energy, even before the wave has progressed half-way between New York and Boston. Even if it were possible to substitute a heavier wire, was to make R equal five ohms, we should have current in Boston equal current in New York multiplied by 6*", it being assumed that the capacity is not increased. Under such conditions telephonic communication between New York and Boston would be impossible even over this heavy wire cable. The same is true even if we assume that the highest important frequency in telephony is much less than three thousand p. p. s. Let us see now how the twenty-oh ms-per-mile cable will act, if we suppose that by some means its inductance per mile is increased to L equal .05 henry. This would be about ten times the inductance per mile of the long-distance telephone-wire between New York and Chicago. The wave length and the attenuation constant of such a cable would be approximately 7L 6.66 miles, [J' .01 miles,

' I was the first to verify this theory by exg It is, so far as I know, entirely new.

periments, and these experiments are described in the first part of Section III of the paper cited above. These experiments were not only the first experiments on record on long electrical waves, but they also form a part of the experimental investigations by means of which theinvention disclosed in this application was first reduced to practice by me. The theories so far discussed recommend strongly the employment of line conductors of high inductance for long-distance transmission. of power by electrical waves, but they do not tell us the way of constructing lines which will have this very desirable property. The additional theory necessary for any advance in this direction was first worked out by me. Part of my investigations in this direction was published in Sections II and III of the paper cited above. Figs. 8 and 9 of the drawings which accompany this specification are copies of Figs. 4 and 5 of that paper. Referring now to Fig. 8, E is an alter nator, and F is a receiving apparatussay a telephone-receiver. L L to L are small coils without iron woundon wooden spools, each coil having an inductance of approximately .0125 henry and a resistance of 2.5 ohms. These coils are connected in series, forminga continuous line which connects the alternator E to the receiving instrument F. In the actual apparatus, part of which is shown in Fig. 11 of said paper, there were four hundred coils. C3 0 to are small condensers connecting opposite points of the line. densers C to (1,... are shown as connecting the points between the consecutive coils to the ground G. The capacity of each condenser was approximately .025 microfarad. The mathematical theory of the flow of an alternating current in such a conductor,which I have called a reactance conductor, is given in Section II of the paper cited above. Its principal object was to find an answer to the question in how far such a conductor resembles an ordinary telephone line with uniformly-distributed inductance, capacity,

Referring now to Fig. 9, the con-.

and resistance. The answer which this thcory gives is perfectly definite. given in the paper is that up to a frequency of one thousand p p. s. such a line represents very nearly an ordinary telephone-line having per mile an inductance of .005 henry,

a resistance of one ohm, and a capacity of .01 microfarad; but even for a frequency of three thousand five hundred p. p. s. a slowspeed conductor represents,if not very nearly, still quite approximately, an ordinary line with uniformly-distributed inductance, resistance, and capacity, the approximation being quite within the limits of my errors of observation, (between one and two per cent.,) and this is true with a much higher degree of accuracy for lower frequencies, therefore quite accn rately for all frequencieswhich are of any importance in the telephonic transmission of speech. A high-potential or highinductance line has not only the-advantage of small attenuation, but also another advantage of the greatest importance in telephony, and that is very small distortion in the sense that all frequencies which are present in the human voice are attenuated in very nearly the same degree. It is therefore a distortionless line. eral rule: If n be the number of coils per wave length, then for that wave length the slow-speed conductor will represent an ordinary telephone-line with the accuracy of the formula Sin. Z Z.

n 11. Thus, for instance, when 'n 16 differs from by about two rule was found by me theoretically and verified experimentally by experiments described in Section III of paper cited above. A conductor constructed in the manner just described was called by me a slow-speed conductor, because the velocity of propagation along such a conductoris smaller than along ordinary lines. Another technical term should be explained now. Much convenience of expression is derived from an introduct-ion of what I call the angular distance between two points on a line conductor. Thus we can say that two points at a linear distance of a wave length have an angular distance of 2 1r.' With this understanding it follows that two points at a linear distance of 9;, where A equals wave length, will given above can now be stated as follows: A

The answer slow-speed conductor resembles an ordinary line conductor with a degree of approximation measured by the ratio of the sine of half the angular distance covered by a coil to half the angular distance itself. It is now an easy matter to pass on to a second type or slowspeed conductor which is better adapted to commercial use for the purpose of diminishing the attenuation of electrical waves. This second type of slow-speed conductor is called here a reactance-cond uctor. Referring to Fig. 10, II is the transmitting and K the receiving end of a long electrical conductor 1, 2, to 10, 11, 12 K. At points 1, 2, to 10, 11, 12 introduce equal coils in series with the line and let the distance between any two successive coils be the same. This equality of coils and distances is not absolutely necessary, but preferable. NVe have now another type of slow-speed conductor. This slow-speed conductor, which I shall refer to as the second type or simply react-anceconductor, differs from those of the first type described in that it has in place of the lumped capacity distributed capacity only, and also it has in addition to the lumped inductance and lumped resistance evenly distributed inductance and resistance. This slow-speed conductor of. the second type is evidently much less of a departure from an ordinary line conductor than the slow-speed conductor of the first type. inference that the slow-speed conductor of the second type .will operate like an ordinary line under the same-conditions under which the slow-speed conductor of the first type so operates, and that is when the value of half the angular distance between two consecutive coils is approximately equal to its sine. This rule is the foundation upon which the invention described in this application rests. A careful research of this matter was made by me and the truth of the rule just given as It is therefore a reasonable.

applied to slow-speed conductors of the second type has been completely verified. The results of this research, which will be published in the near future, will be explained in language devoid of mathematical symbols, 1

the object being to explain in as simple a manner as is possible the action of a reactanceconductor. I shall employ again the analogy of a vibrating string. In Fig. 6, A B" O" is a tuning-fork rigidly fixed at its neck C.

The full line B D" represents a heavy flexi' ble inextensible string which is under tension and fixed at D. The circles, equally disj tributed over the string B" D", represent equal masses attached to the string.

period, so as to develop in the beaded string a vibration the wave length of which is equal to or greater than the distance 13 D", some-- Let i now the tuning-fork vibrate with a suitable resistance, and mass which the beaded string has. The mechanical vibration in such a string is a perfect analogy to the electrical vibration in an electrical conductor represented in Fig. 10. In this diagram the alternator H is supposed to develop approximately a simple harmonic electromotive force. One pole of the alternatoris grounded at G and the other pole is connected to a wire conductor. At equal distances 1 2 to 10 11.12 are inserted in series with the line twelve equal coils. Suppose now that the electromotive force impressed by the alternatordevelops in the conductor an electrical vibration three-fourths the wave length of which covers the distance oragreater distance. Then the law of flow of the current in this conductor will be the same as the law of distribution of velocity in the beaded string of Figs. 6 and- 7. This mechanical analogy, besides being instructive, offers also an inexpensive method of studying the flow of current in long wire conductors. Afew experiments with beaded strings excited by tuning-forks will convince one soon of the soundness of the physical basis on which rests the invention described in this application. A reactance-conductor is a long electrical wire conductor having preferably reactance sources in series at preferably e'qual intervals. Such a conductor, just like the reactance'conductor of the first type, is equivalent to a uniform wire conductor of the same inductance, capacity, and resistance per unit length when the angular distance between two successive coils is such that one-half of this distance is approximately equal to its sine. Such a conductor will therefore possess low attenuation and inappreciabledistortion if its reactance per unit length is large in comparison with its resistance. This condition can be readily fulfilled in conductors of this kind. When the interpolated reactance sources consist of simple coils, they should be made preferably without iron cores, so as to avoid as much as possible hysteresis and Foucault current losses and current-distortion. This can be done in nearly every case without making the coils too bulky or too high in ohmic resistance. If for any special reasons coils of small dimensions per unit inductance are required, then iron or preferably the finest that is, springiest-quality of steel should be employed and the magnetization kept down as much as possible. For telephony the angular distance between any two successive coils should sufficiently satisfy the rule given above for the highest frequency, which is of importance in the telephonic transmission of speech.

I shall now show how the rules explained so far in this specification can be applied in practice by working out two particular cases, giving all, the instructions which I believe are necessary to those skilled in the art.

'(a) Suppose that it is required to transmit speech te-lephonically over a distance of three is .6 ohms per mile.

I ,be calculated from the formula thousand miles of wire stretched upon poles. The total attenuation factor over that distance should be about the same as that over the best New York-Chicago circuits of the American Bell Telephone Company, whichis (leakage not included) about e for the highest frequency of importance in speech namely, about fifteen hundred p. p. s. It is proposed to state first the conditions which will give an attenuation factor of 7 with a length of three thousand miles. Let

[f the attenuation constant.

Z distance 3,000 miles.

539005 the attenuation factor 6 Then Assume that a copper wire of four ohms per mile resistance is used and that the additional resistance introduced by the inductance-coils The total resistance per mile will then be 4.6 ohms. \Vhen the reactance per mile is sufiiciently great in comparison to the resistance, we havethe followingsimpli fied formula for the attenuation constant: g R O a wire of 4 ohms per mile is .01 microfarads,v

the wire being hung as thelong-distance airlines of the American Bell Telephone Company are hung. The inductance of the wire can be neglected, and I shall consider L as due solely to the inductance of the inductance-coils. The value of the inductance which will satisfy the assumed conditions can just given, as

follows:

0 n )0 I 3,00 /3 0,0 2 103 L- 15 Hence L .2 henry.

Having calculated the inductance per mile, the next step is to calculate the wave length for the highest frequency to be considere d namely, fifteen hundred p. p. s.

15 miles, approximately.

.of two ohms per mile and wind it into a coil of five inches internal diameter and twelve ductance with small volume, steel or iron cores should be used to avoid excessive ohmic resistance. Coils having iron cores are a source of three kinds of lossesviz., those due to Faucault currents, hysteresis, and ohmic resistance. Each one of these losses has to be very small if the coil is' to be efiicient. I have found that this can be accomplished at any rate when it is required to transmit only small quantities of energy. If the core is finely subdivided, Foucault currents are negligible, especially for exceptionally-weak magnetizations, such as will be employed in the case before us. It will now be shown that hysteresis also can be made negligibly small. Let the wire have a resistance of five ohms per mile. According to present cable construction the capacity per mile with wires of such size is very nearly three-tenths microfarad. Introduce ind uct-ance-coils at proper distances, so as to make the inductance threetenths henry per mile, and suppose that these coils add one ohm per mile, thus increasing the ohmic resistance to six ohms per mile. The wavelength for a frequency of fifteen hundred p. p. s. will be A 2 miles, approximately.

2,000 [1 6. hence -aooos I s To secure a close approximation to the rule above given, it will be necessary to introduce sixteen coils per wave length or eight coils per mile. The inductance of each coil will then be .0375 henry. The resistance of each coil will be .0125 ohms. Employing cores of iron or well-annealed steel, coils of this inductance can be readily made which will be small enough to go within the sheathing of a submarine cable as these are constructed today and at the same time show negligiblysmall Foucault-current and hysteresis losses.

In Fig. 11 X is a ring-shaped disk. Its internal diameter is 2.5 centimeters and its external diameter is 6.5 centimeters. Its thickness is .002 centimeters, or about .005 inches. It has a narrow slit p. q. A core is built up by piling together a sufficient number of such disks to give the required length, which we will assume is ten centimeters. In-Fig. 11 a transverse section of such a core is represented. Wind this core with two layers of wire having 8.5 ohms resistance per mile.

Transmitter-coils Let each layer have forty-eight turns. The length of the-wire will be eighty feet, audits ohmic resistance will therefore be a little more than .125 ohms. Eight coils per mile will therefore add one ohm per mile to the resistance, making the total resistance six ohms per mile. To calculate the inductance, the permeability of the iron must be known. In telephony the maximum value of the current at the sending-station is generally less than .0001 amperes, or .00001 units of current in the centimeter gram second system. The magnetomotive force of the magnetic circuit is for this value of the magnetizing-current:

Theintensity II of the magnetizing force will be where Z is the mean length of the magnetic circuit equal to ten centimetersroughly. Hence For excessively-feeble magnetizing forces of this kind the magnetic permeability ,u of firstclass iron is about 180. (SeeEwing on llIagnetz'c Induction in Iron and other lVIetaZs, p. 119, especia'lly Sec. 87.) The intensity of magnetic induction will be B 180 X .0012 .22 lines of induction pet-square centimeter. At this excessively-low induction there is no h-ysteresis (see Ewing, cited above, Sec. 89, especially top of page 128, and Sec. 180.) The inductance of the coil can now be easily calculated. The formula is 4 7r 3 ,u L

where s number of turns 96.

q cross-section of core in cm. [1 20.

,u permeability I 180.

Hence L .042 henry.

work disastrously. The limit of magnetiza' tion permissible will not, however, be passedeven if the magnetizing-current is thirty times as large as is assumed above-that is, the magnetizing-current can be as high as three milliamperes(See Ewing, Sec. 87,) a strength of current which is capable of operating telegraphic apparatus. Itshould also be observed that the iron core represented in Figs. 11 and 12 can be made by winding'very fine iron wire, the plane of the windings being perpendicular to the axis of the cylindrical tube which constitutes the core. The advantage of this core is that it still further reduces the Foucault-current losses and also prevents magnetic creeping. (See Ewing, end of Sec. 89.) The cross-section of the wire core would have to be made larger than that of the plate'cor'e to allow for the more imperfect filling up of the available space by the substance of the wire.

The invention has been explained with reference to telegraphy and telephony; but it is also applicable to the transmission of power by alternating currents.

It-is to be understood that only the simplest and most direct manner of increasing the reactance of the line has been shown-viz., by introducing simple coils. There. are, however, varionsother ways known in the art of producing the same eifect. For instance, we may have each reactance-coil provided with a secondary winding and place a condenser in circuit with this secondary. By properly adjusting the capacity of the condenser the effective inductance and the effective resistance of the reactance-coil can be increased or diminished within somewhat wide limits; but the simplicity and uniformity attainable with the simple coils makes it, in my opinion, the best method. In all of these arrangements the reactance of the line per unit length is increased by introducing reactance at various points along the line, referred to in the claim as reactance sources. The particular means of increasing the reactance is not important, the fundamental idea of the invention being to transmit energy with small current by adjust-ing the reactance of the line, thereby diminishing heat losses and resulting attenuation. The equivalence between a reactanceconductor of the second type and its corresponding uniform conductor holds true with respect to free vibrations also. It holds true also for periodic unidirectional impulses, because, since each unidirectional electrical impulse employed in ordinary telegraphy and cabling can be represented by a convergent series of simple harmonic impulses which are harmonically related to each other, it follows that a reactance-conductor will act, like its corresponding uniform conductor for ordinary methods of telegraphy,by unidirectional electrical impulses if the reactance-conductor satisfies the rule given above for a frequency the period of which is snfiiciently small in comparison to the timeof duration of the unidirectional impulse. Their ratio should equal twenty-five or more.

It "should be mentioned here that I have so far described reactance-conductors which are a close approach to a uniform conductor for tromotive force which is to be impressed upon the line and the'form of the resultant current-wave and by the amount of attenuation with which it is proposed to work in a way which can be easilydeduced from the rule given above.

It will be seen from the foregoing description that the method of diminishing the attenuation of electrical waves transmitted over a conductor consists in distributing along the conductor reactance sources of sufficient strength and making the reactance sources sufficient in number relatively to the wave length to secure the attenuation constant and the degree of approximation of the resulting non-uniform conductor (consisting of the uniform conductor and the distributed reactance sources) to a uniform conductor, as

the requirements of the particular problem necessitate. The conductor will then act with respect to the electrical waves within,-

the proper limits of periodicity--that is, for

the shortest waves to be considered and all I longer waves as a uniform conductor having the same resistance, inductance,and capacity per unit length. It will of course be noted that the character of the waves to be transmitted asdefined by the periodicities contained in it is the controlling factor determining the distribution' of the inducta ce sources.

It will be seen from the foregoing statement that this invention applies to f electrical wave transmission and involves the construction of a wave conductor. If the length of the conductor relatively to the wave length of the current transmitted is suificiently great to permit the development of the wave phenomenon, then there is wave transmission; butif the conductoris too short for this there is mere ordinary direct transmission. The distinction is that if there is no perceptible development of waves there is no perceptible attenuation,and therefore the invention does not apply. The term waveconductor is intended to indicate a conductor which forms a part of a system of conductors over which electrical energy is transmittedby electrical wave transmission. The use of these terms in the claim is intended to bring out the distinction here stated.

, It will be noted that Ihave herein described a method of modifying a conductor of uniformly-distributed capacity, resistance, and re'actance in such manner as to diminish its attenuation constant by increasing its efiective inductance without affecting seriously itseharacter as a uniform conductor with respect to the Waves to be transmitted. This I accomplish by distributing along the uniform conductor reactance sources at periodically- -recurring points, the distance between the points being determined by the considerations heretofore presented. There resultsfrom this method a non-uniform wave-conductor consisting of a uniform wave-conductor having reactance sources distributed at periodicallyrecurring points along its length in such mannor that the resulting wave-conductor is equivalent, within proper limits, to the corresponding uniform conductor from which it is produced, except that it has increased efiective inductance. It will of course be understood from the foregoing discussion that the distance between the reactance sources is determinedby the'wave length to be transmitted or the wave lengths which constitute the components of a complex Wave to be transmitted and by the required degree of approximation to a corresponding uniform conductor with respect to distortion and attenuation of Y the waves to be transmitted.

The apparatus is not claimed herein. This case is filed as a divisional application of my former application entitled Impro"e-.

ments in the art of reducing attenuation of electrical waves and apparatus therefor, filed December 14, 1899, Serial No. 740,238, pursuant to a requirement by the Patent Office that the said application be divided, so as to separate apparatus and method claims.

It will be obvious that many changes can t be made without departing from the spirit of my invention. Therefore, without limiting myself to the precise details shown,

What I claim as new, and desire to secure by Letters Patent of the United States, is

The method of diminishing the attenuation constant of a uniform wave-conductor which consists in increasing the inductance of the conductor su fliciently to secure the required diminution of the attenuation constant, by distributing along it inductance sources at periodically-recurring points, the distance between consecutive points being such as to preserve approximately its character as a uniform conductor/with respect to the waves to be transmitted, substantially as described.

Signed at New York city, New York, this 26th day of May, 1900.

MICHAEL InvoRsKY PUPIN.

Witnesses:

TnoMAs EWING, J r., SAMUEL W. BALCH. 

